Weighted Hardy spaces and BMO spaces associated with Schrödinger operators

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Abstract

In this paper, we characterize the weighted Hardy space equation image related to the Schrödinger operator equation image, with V a non-negative potential satisfying a reverse Hölder inequality, by atomic decomposition and Riesz transforms. We also get a characterization of its dual space equation image through a weighted Carleson measure. Then we prove the boundedness of some classical operators associated to equation image on the weighted BMO space equation image.

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